Solve the following equation by factoring. $$ w^{2}-2 w=0 $$

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To solve the equation $$ w^{2} - 2w = 0 $$ by factoring, follow these steps:

1. **Factor out the common term:**
   
   Both terms on the left side of the equation have a common factor of $$ w $$. Factor $$ w $$ out:

$$
   w(w - 2) = 0
   $$

2. **Apply the Zero Product Property:**
   
   The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, set each factor equal to zero:

$$
   w = 0 \quad \text{or} \quad w - 2 = 0
   $$

3. **Solve for $$ w $$:**
   
   - For $$ w = 0 $$, the solution is straightforward:
     
     $$
     w = 0
     $$
   
   - For $$ w - 2 = 0 $$, add 2 to both sides to solve for $$ w $$:
     
     $$
     w = 2
     $$

4. **Conclusion:**
   
   The solutions to the equation $$ w^{2} - 2w = 0 $$ are:

$$
   w = 0 \quad \text{and} \quad w = 2
   $$
The solutions are $$ w = 0 $$ and $$ w = 2 $$.

Solve the following equation by factoring. \[ w^{2}-2 w=0 \]

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